Answer :
To determine the leading coefficient and the degree of a polynomial, we need to identify the term with the highest exponent and its coefficient.
Let's break down the polynomial: [tex]\(18x^8 - 23 - 6x^4\)[/tex].
1. Identify the terms of the polynomial:
- [tex]\(18x^8\)[/tex]
- [tex]\(-6x^4\)[/tex]
- [tex]\(-23\)[/tex]
2. Find the degree:
- The degree of a polynomial is the highest exponent of the variable [tex]\(x\)[/tex]. In this polynomial, the term [tex]\(18x^8\)[/tex] has the highest power, which is 8.
3. Determine the leading coefficient:
- The leading coefficient is the coefficient of the term with the highest degree. Here, the term [tex]\(18x^8\)[/tex] has the highest degree, and its coefficient is 18.
Therefore, for the polynomial [tex]\(18x^8 - 23 - 6x^4\)[/tex]:
- The leading coefficient is 18.
- The degree of the polynomial is 8.
Let's break down the polynomial: [tex]\(18x^8 - 23 - 6x^4\)[/tex].
1. Identify the terms of the polynomial:
- [tex]\(18x^8\)[/tex]
- [tex]\(-6x^4\)[/tex]
- [tex]\(-23\)[/tex]
2. Find the degree:
- The degree of a polynomial is the highest exponent of the variable [tex]\(x\)[/tex]. In this polynomial, the term [tex]\(18x^8\)[/tex] has the highest power, which is 8.
3. Determine the leading coefficient:
- The leading coefficient is the coefficient of the term with the highest degree. Here, the term [tex]\(18x^8\)[/tex] has the highest degree, and its coefficient is 18.
Therefore, for the polynomial [tex]\(18x^8 - 23 - 6x^4\)[/tex]:
- The leading coefficient is 18.
- The degree of the polynomial is 8.
